 Quote by joe_cool2
The equation for force I must use, then, is:
F = ma + v(dm/dt)
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Why is that the equation you "must" use?
There are three choices for addressing variable mass systems in the context of Newton's laws:
- [itex]\vec F=m\vec a[/itex], in which case thrust is an external force,
- [itex]\vec F=\frac{d\vec p}{dt}[/itex], in which case force is not frame invariant, or
- Newton's laws are valid only for constant mass particles, in which case Newton's laws do not apply (at least not directly) to variable mass systems.
Your definition of force, [itex]\vec F = m\vec a +\frac{dm}{dt}\vec v[/itex] corresponds to choice #2. This yields a force that is neither frame invariant nor equal to thrust. Most people who work with rockets use option #1 or #3.